{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 感知机的朴素实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class Perceptron:\n",
    "    def __init__(self):\n",
    "        self._w = self._b = None\n",
    "        \n",
    "    def fit(self, x, y, lr=0.01, epoch=1000):\n",
    "        x, y = np.asarray(x, np.float32), np.asarray(y, np.float32)\n",
    "        self._w = np.zeros(x.shape[1])\n",
    "        self._b = 0.\n",
    "        for _ in range(epoch):\n",
    "            err = -y * self.predict(x, True)\n",
    "            idx = np.argmax(err)\n",
    "            if err[idx] < 0:\n",
    "                break\n",
    "            delta = lr * y[idx]\n",
    "            self._w += delta * x[idx]\n",
    "            self._b += delta\n",
    "    \n",
    "    def predict(self, x, raw=False):\n",
    "        x = np.asarray(x, np.float32)\n",
    "        y_pred = x.dot(self._w) + self._b\n",
    "        if raw:\n",
    "            return y_pred\n",
    "        return np.sign(y_pred).astype(np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "准确率：    99.0 %\n"
     ]
    }
   ],
   "source": [
    "from Util import gen_two_clusters\n",
    "\n",
    "x, y = gen_two_clusters()\n",
    "perceptron = Perceptron()\n",
    "perceptron.fit(x, y)\n",
    "print(\"准确率：{:8.6} %\".format((perceptron.predict(x) == y).mean() * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dDTHzVGCjsqyKm3rfR1lRBR8deo24vt28bVKj5FLKx2y1i/x0aOhLNFcyyu3r7COTnzjg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\noooKLTo1ocZ51fh44iI2/ZxPTc1gCAMmsTtITxv/qBaDROP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      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e85d93ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Lb6EHh99E3NEVoOpXt7P1G5djetOQQuBs62TG7/85KdJbh4MSdsWkpuHs45B9GkJIl0Hn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\nJGK3nhuA6CCzZ+ovPIXWJYc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Vg0w7/PvMOflSNEfqB6RCMRkYsaWAEMIBbABOBGqBd4FL\npZRrUl2jLAVGhuUXtD3oxfe8Bz3DIvuSLrwnhPotDopsd7D9skKskICYAE0iDEnpb1tJP2rgMErn\nsx4afp7TK5yz++9GgFMidEnJr1rxHjv+Dn9TrSJVoUjFYC0FRsUrRghxBnArdrrj3VLKX/R3/r4u\n7LEmjabfZ9H1mgfhkGSeFSD/a52Dyk4ZCdE6ndZ7vIQ+cOGsjJF7hQ/3vMF3pvEvd9F6RwbhzU4s\nn5YQ69fSLWa+uCtpmuVYMxxxlxJVKauYVIyrV4yU8llg31XqIWAFBdsuK8Rs1cEUSKDjkXRCawwq\n7m4aU6FxlpgUfa9j2NenLw6TvjjMzq/kE1ieGFiXQOhDF2mLxj+UMdjcdjPmofb9a2jbch6WZeAt\neJeKRTfizqoZh1kqFOODqjwdZzqfTbM3I809Ci4jGuENTkIfTsBSdzgYqd8shKP/t45orU7dj3Oo\nOb2YbZcX4HtxfHdea179K60152OZHpA6XY2HseH5B4gG88Z1HgrFWKKEfZwJrXXG+az0ICG8MYXT\n1wiQUfC94KHpT5l0PJaG5R/5K0H2+X7bwqAPmkvi3j95Hj3YTpTbLi3CtzSNWIOD8BoX9T/OpfUe\n74jnNBiCbXPwt+yPtHo/TDQs06B508XjMgeFYjxQwj7OGDNjydMVNTAqR7frkekTbL24iPrrc2j7\neyaNv8um5qxiIltHFoFLPzZE5pkBhMuyv9IsNK9F6e9bEP0kx7TenYEVEHGxeRnSaPl/mVjBkT9w\nBsqQCflmIpIUJUnLTbBt7ojvr1DsLShhH2eyzvYjDOLzwh0SZ7GJZ5Rj0823ZRKtdSAD9q9ZBjWs\nTo36n+aMaFwhoOgH7Uy7v5GCqzso+lEbM/9bh6ef1TpAYKUrLgTVM54G0R2Df9hICVaEpGZk/Ym7\nO3MzUiY+eYQWwpOzbtD3Vyj2dpSwjyKxJo22+7y03JVBeEPysIqeKan8eyPuAyJ2XrlDkr4kRMUd\nTaPeqKLrf2nQ135ACkLrDMyuka+QjRkxsj/pJ/O04KAyelJZDsioQM8bnB1BxxNp1JxSwqYjyqg5\nsYS2h9ITBD6VuHuyN5Kevwqh9U7JNNH0MPmzHxrU/RWKyYBqtDFKdD7voeEnOSBBmoLWOzPIPN9P\n4TUdCZkuxowYlXc3YUXs1W+qJhojJtWDwoLIJieeA/tfYY82uZ/1EVxlxFkbCMMi7cgwjryBnSE7\nnvXQ+JvsnuvNdp3mP2QhNMi+yJ9wvul24Z87AxGJ4l2/BWFZVB3zVWpXfYfWLedjmS4yipZTfsjP\ncbqVzYVi6qB6no4Cpk9Qc0pJgpeK8FiU/aFlQtL/AJpuzaL9wXRkpPe8JAgQLonn4DBlv29J+mCJ\ntWl0PplGZJsDzwERMk4Z3Kp8IDqeSqPp5mxkFIgJ0o8NUnx9W4rK1nhqzi4mVpu4FtFzTapeiHdE\n7MxppbFkM8I0AYGIxai66S7SanYkXK9QTBZUz9NxJPC22y7N6oMMCTqf9Qxa2MMbHTT+NpvgBy60\nNIvsi7rI+4Jv2Cv6vC914n/bILLR6C4UFfaXtOcWfM9F6z8yyPuCL+660MdOdn6+ABkDGdbw/dei\n5fZMpt3biJ4zMs/1rLMDZJ4eIFqno2dZtjfOIIk1JN+ZNVs1pEnPxm3EFaKxcidSM+JMizZf9wX2\n++rP0GKTx4VSoRgOKsY+1gwylB3dpbP9s4UEV7ggKrA6dNruzaD++uFvdGoeiTF9t4glTkSGNTr+\nk97zvRUQdDyZRu3/5WP5Rc8biAxqxJp0mv+aOey59EY4wKgwhyTqYNsaJ8NRZMZl43TktSKTmJZJ\nTaPzQJX9opj6KGEfBdKOCEGShaxwSTLPGFzf0bb7vN1e5/GpgF0vphFNsVIdDP7X3NBPq7fd/uqh\n9U5qTiuh4dfZmC0aCQ+CmKDrpdS9V8eDgm92JKSKCrdF/tfjq2ktPZb8gSoElmdiP4NCMR4oYR8F\ndK+k+MbWnrxudIlwWWSd78dz8OA2KENrDNucqw/CkESHmXc+4PaJQ+I9IYiUUHdNnl0RG0oi6rvn\nkqQn63jiPTZEya9bMWZGEYbEOS1K8Y1tZJ4R37kpvTMLYSb+aUtdw7tm43hNV6GYMFSMfZTIODGE\n54B6fC94kEGN9KODuGYPvuDIVR21xb1PnreMCJwVQy9csvyCnV/N7+621LfdHqBJHAUmeV/tJLrN\nQayl/2f87gfVROM9JoT3mP4dJNM7MnH70wilB5C6BRK0cJj8Z1/DaB2+V45CMVlQwj6KOPItci4Z\nnvjlfNpH59NpyF4VmMJlpwI6S/ds9lkR8L/sIVrrwFUdJe2IUNL896Zbswivd/Z5UHRnxKRZ5H3J\nR/aFfkJrDNruT09st9czCWln0BwYIedKX/Jz9jIEgrLNM/HltOPLbkezNIpu+zUZazdN9NQUinFB\nCZxLwmcAACAASURBVHsKpITwOiexJh33fhEc+SPLBhkIo9Kk4vYmGn6ZQ3i9E+GSZJ3nJ/+be1aY\n0V06268sxAoIZEgg3BJneYzKu5rQ0uPDJJ1L05DRxFZ26JKqV+rQdGj6YybtD3qRofjYfg9OC+/x\nIXI/48M9v397XysMbfdk0PFEOliQcXqAvM/5BpXGOBYIBJltOWS2dW8+n/lXWKt82xX7BkrYkxBr\n0tj5lQKidTpCt8MhWZ/souDqxGKjkSAlhD4yCLzjQs+yyDg5yLT7GpEmoCV6hdf/NAezdY8PugwI\nolscNP81k8Lv9gkxpFqBW3YJf2S7g/b7M/o0p4bdDTSER+KeH6H4htYB/dWlhNqvFtgGZ92ZNO33\nefG/4WbavY2IAf7KYk0all/DWRkb9erb3gzW2lehmOyozdMk7Lomj8g2h+2t0qUhI4KOR9Lx/Xf0\nMiqkBXXfy2XnV/Jp+VsmTb/PoubMYgLvuhB6oqhbQUHwA1dCcwsZ1fAtTUsYP+2IUGIrPE3iWRRG\nCAi85UrZx9S1MELpLS2U3948qKYZwZUGofXOuAItGdGI7nTgfz21LW+sSWP7ZwvYcnYJ2z5dSM0p\nJXT1c/5oMNIm2ArFZEAJex+iDTrh9Uk2MUMa7fePnr2s73kP/jfctoWvJZAhDRnU2HVNrl2V2Zd+\nIhrJsl8Kr21Hz7J60gOF27LDNRZsPKqU5r9k2W8GfXGC9+gQ6YvDg347Ca0xksboZUAjuDr5k0FK\n2PmVAkKrDWREIIMaZqtO3bW5RLYMMwsoBp1Pp7Hza/nUfjuPrmXuIRuFKRRTARWK6YPlt+PQyWLO\npm/0noOdT6Qn9WWXpiC02sBzUHyapJYmcS+I2M04eq/anRYZpybmyjtLTaY/Xk/nM2mE1xs4SmK0\n3ZtB8D0XSNH9nEhUPaFJMk9PHE9KiNXpCKdMaJrtLDYRhkT2SdcUbgtnSfIqz9Aap90Au+8DNCpo\neyidouuGlr0iLaj9Rj7BD4yen2tguYus8/2JYSqFYoqjVux9MCpjiGQdgpwW3uODicfHkeKftdqr\n8DQLkIg0C6PCJP+rnUnP1zMkOZf4Kb6+DRm0Q0rxxUp2KqTwWIh0Owe/6MdtOMvixTj4ocHWc4rZ\nemGRHTa5tJDIjj1FU+nHBu0c97jQjkQ4IeOU5AVaZpOePJ5uCmJ1Q19v+N90x4k62BWzHY944+aq\nUOwLqBV7H4QDin/aRt0Pcu3wgikQLgs91yL3M11DGkvG7BVoMvOszHP9CUIEIPTUXYiMCpMZT9fT\n9aKHaK2OqzpK+tGhATcnwRbnZBuqmleSfZkP16zo/2/vzMMjK6v8/zn33tqrsied3hdAFBCVVUDH\nhUX8DaCCqMOgCIygg4j8WBRQRhSVR+aHIOCD7JuIgAJjiwoIDriACA46AkoDvSedpZKq1L7c9/fH\nraRTqVtJupNKpSvv53nyPN213Hpvdfp7zz3vOd9D8KAsZrh8rYVBw6mHT21fZ/YfHjb9Wydr1vYi\nHhi6IzJuUIbzfquryNJrBzAjVfL4e+XdSywNhVXFOmAykk/73SdTGYrUH/14l5eXoeqNVE0jo4Xd\nhfB7M6y4q4/he8Pkt1gED8nQ/JFkhehVw85A/3+2EF8bQhXAs6LAokuGCO6/XbAjR6ZJPBEg+Vs/\nKivOXYLAkiujkwq1EVA0HTM9m4Lx+PbIk/mry95BHpo+mMK73D1lEv9ZECbqrC3YSYPk7/1Y3UWi\nt0UgVy6qhQFzsm0BPIuKNH044ZRHjnfFtCH+YAjPouIOXUjNliJYqrJ71wCzyb1UVYu7plHRwl4F\n324FFl0yvFPv7bmoneQf/FAqJcyv97Dl7A5W3N2Hb42jkmLA4iuiZP53fLljCrO5NnXfrf+aqGiA\nwrKdrlYXK4NR8j3WBNvfEkUo9JvOXYdb5G3DxpO7CB2WwfApIkenCb27vJmq60sxBBi+PzwuReTU\n6A9+v5nmY1PTdpNsOjbF0J2Ryjy/AaF31zeFptHMNTrHvgMoBekXvcTXBsn83d1LN99jOqWEOZdN\nwTsjZY+JQOCtOdpPH6Hlo8maiTo4ewfLvj+Ad/dcKRfubBDnt1hsOKmLnotbXatkAvtlXQdXI+Df\nJ+ccxnXZAnkh+ZsAI78K0XNxGz1fbkMp5zuK/yJA6g8+ClHT3aTMo0g955v++S0r0n15dGz+qoRs\nzNYiS7/fjzFJBaWukNE0IjpinybFuLD5zE5yGy1nz9EG/1tzLP3eAMY4/clvNREvqIlp8qKQfW32\nRiWpIiR+HWDksQBGUDmGY1NMRAq8Lceq+/rY8C9dZF/1QEHGItzEbwLEHszR8tHyXHTk/WmiNzeR\n38RY5C5+m+DBWfxvzoMNQ/eGIetqp7h9vWmD5O/8bP1SG6mnAk7aRJx9CAxVUZ8vgBHasW7fyOEZ\nQodtJf2iD/EoAm/LTTpcexSdktE0GlrYp8m2b7Y6wjzuVj/zFy+DNzTRec72qhTvqoJLNydgKQJv\nnXzghspD9lUPRlDhXVV9A1EVYcvZ40r7RDHyWIC20+O0nz55Xjq/zST3hqey0SljMHx/qELYxQMr\nbu8jekeYkV+GEI+i+YQkLR9zPse/V57WkxIM3RZhKvN5lRaSTwacPH+ufLO1AksRPGjHJ08Zfggd\nXJ+JVRrNfEGnYqaBKkDiyUBFLlplDWIPhcoes9ptmo5JlvuGi8LwKVpPri66id/4ee2IJWw6o5MN\nJ3Wx/qOLqpbpJZ+eUNqnnAan6E3NFAbGlfsVIbvOIrd5+3FUlsqO1NHnMu7CbIQUHf8+wur/6mXV\nT7bRelKibIO38+w44Q+kSvX/U1Cc+BkTBd7J7XRdMFy7WbAu6JSMppHQwj4NlI3rIA3ANTrvumiY\n9jPjmJ0FJGATPCTD8jv6ylwax5N7w6Ln4jbsEQOVMlAZg9x6i82f7XQ+ewIjTwTcS/ssRepZJ6Gc\n/J2P149azMZPd7HhxEVs+EQX+S0mVneVsXAem/BRO7/J2P0fQwQPyjie9KU6+wqqBvTjTcicPw8/\nMHtdvhrNQmPBpWKUqvRhmQrDC/69c2T+11u+0WcoQu+q9AYXE9pOSdB2yvTK9YYfcLHNtYVizCD9\ngq9iZqoZsd3z0gJG2Ca3yWTrBe2ozLja83UeNn2mk9B701Ch7QqjyabtlJ235TX8sOz6QXLrLXLr\nLYojBv3fadku7wUIHZ4m+USgbF3VyPx1GiY1s4zOtWsahQUh7MqG6K0Rhu6OYMcF75oCnRcM71Au\ndtFXh9h0Whcqr1BZw/FeCSo6z528Xb044lSeeLqLmC3uYX+hr7K1fuz9LgMwmj+cJPbTEGrihqXh\nmH8NXt9cUfaHLRR6TWL3hqkMnQUzqKZdp++GKkDiKT/Zf3jxLisQOTJF5KgUqT/6UXkIHpRFLMWm\n1z1jBmuYqnSRcWmcCtWuQmgytLhrGoEFIez91zQTuz80FinmXvew9dx2lv1ggECVLs+J+HYvsOqh\nXmIPBcmt8+DfJ0/TscmqnZXKhv7vNhN7IIxYCjsrGGEbVQTfmgIdZ8XHIvHQYRmSv3fpnCwI/lKl\ni50WRh4PkN9o4dsjT8e5wwx8txUs5ciiqVh67SCGF/K9ZpXa9Oq3KoV+Ezu9vUs2v9UkvjZIcdgg\neGiW0KHuAz3AqRja+OkuCn0mKiVIQNF/dTPLb+8j/O7yO5oVd/Qx8miQ5O98mB02dtxg5FeBMmdI\n8du0fGzXGOqh0cxHGl7Y7ZQQuy9UJhzgbBQO3hhh2bWDACSe9hO9KUK+x8K/V46Os+L43lRus2i1\n2bSf5qRX7CyknvOjchA8MFsh8MP3hIn9xImqRyNre9jZxMy8aLLl7HaWXDVI6JAskaNTDN0dIb+F\nsXVKwKb5w0k8i4rOgI1TSgM20gYStLHaiqy8r5fcOg/iV6gi9F/ZTG6ThdHs+L5MPOfqKFROeO2I\nxXRdPIQZVvRc1IYqOrXosYdDBPZ1SjvdNjQHrmsmv8UasyxQaaGYVWy7rJXlNw2UvXbUPyZ4UGbs\nDsbOOPXu4nXWET48Tftn6ifsOmrX7Oo0vLAX+k1wLS4RcqW68tjPgvR9u2Usok/+1k/qOR/Lb+vH\nv2elh27qeS9bz+3YbglbcDZMm4/b3uofvSs8aS5ZZQ36r2ohdP82DD+suLOP4R+HGHk0iBGyafl4\nkvARzmZm79dbKQ6NH7BhkM8J0Vub6P6PIUae8NP7lbaxz7NjptOEZNlQmErcS06WtiPIfZe3gkHZ\n2lXaIP0XL/FfBmk+ttLOYOSxQKUPjS2k/8dXdhegFERvCxO9rcmxKTCh7dNxFn87SqHfIL/Jwrui\nUOEeWQ+0uGt2ZRq+KsbqKrpsFgKi8O6ex846KZMyEVZOlD1wbVPF2+y0sOWcDmcAR7L0kzXo+3YL\nufXbr5N2fOrOmNxrFoUh53ONoKLt1AQrf9TH8psHiByZRsSpbU8/Xzlgg4KQeNwZ/NF/VUvlRUQJ\nZrM9SQni9u7Tskdz4u6tnjaI/7xyoMeUjHN8HL43RPTmprHvTKUMorc2MXxPCE+XTXD/3LwQ9VF0\nCaRmV6Xhhd0IKFpOSpTXlZdI/c7PusOWYsddvgYlZF6qrMxIPuXen64KQmztduHz7z29jdme89un\n9TpXSsJf6HG/iBTjJq2njuBaemgoxO/yuJJK06/Rj/O5XyQiR6fAM+H7NRSB/bIYfme/If5IgP7v\nVl6AVMZwIniNRjNrNLywA3ScFaf9s3HMtqITwRqqFLCKEwlXCRI9XZWhvp0S92bJItjjBnF0nhdz\nPFaM8Y03E3EuHvlt1aN78UDwnZnKyFsUdlJY9/4lVRt5zFIJo9leLP9803Y2ZSfeBYDT6u+Kwr+P\n+8Wq46w43lUFp37ddHzizfYi3V8bAqDnoja2fbO1qtlYccgom3Rkp4X42iCDN0dIPutzreXXaDTV\nafgcOzgOf22fStD2qQRD94UYuKZ5QgWKM3BifFpC/DZtLht4wYOzrqWJElBlgzj8b8mz4q4+ordE\nyLzsJb/FdB8wbSrsmAGLqjQOUSq1/HQXxbjhbMSO6bSgkuJcPCrq2hXFuLD+w90s+mqU5FMBEk84\nG5RNH0nSduoI0VuaGLo7PPZdiN9GLLAT7tf76E3N5Nd76P7GUFmFjBlWrLynj+Qf/ORe9eBZWiD0\n3jSG15mUlHzaP+l+g2dFYay3IPu6xabTO52UUFYQv8K3e55lN0xu5lUrdK5dsyuyIIR9PPk3rCoD\nGXDSE5ZCLOg4K0bk8MpOTM+SIq2njDB0V9gRWSVOd+nBGUf0x+FbU2DxN52odf0Ji8i9Mb7Dcjve\n1W5DTsd9ZpfN6od7STztJ/bTkON6mB/vYS5g2ohPlSpwSj95oTjo2AiveaSHRV8ptyHu+FycwNuy\nDN8fxk4YhI9KkVtnEftp2L31v2StEHswR8sJEzxlTGdWKhMatlLP+dxtfUff57fpPG97L0DPRW1O\nakyNbhQL2b97GLorUtdKGY1mV2JGwi4iVwLHAjngNeBUpdTOmZjPEb635JGAXTm5yKdYfOUAvtVF\nrI7ipD4lHZ+LEzw4Q/zhEHZWaPpAitB7MlU7WnObTaccsELUFWZ7kdwma8ynvRrigcj7M4w8EiwX\n9RKGD0JHpRj5ZRAmer4oGHk0SMuJyYr3hQ7NEjp0+wUpt8Ei/rOQU+rogsoYxO4PVQh7NcwW2ylj\nTFeeu7W0QPelwwQPdD6/0G+Q3+CpsPFVWYPobREC+2XLhpXMFTpq1+xqzDTH/hiwj1JqX+AfwEUz\nX1JtiRyVcibqjMtZi9fGuyZP6JAcnsWTi/oowf1ydF82xJIrooTfV715ByD7ihc87jn2wiaLjSd3\nkfz99LzHfXvmEW9l0lnZYPqVa7pHZYS+/2zh1UOWsOX8tklz+t6VBZZcNYjRWqCa86LtatE74TMV\nxH8ZYPi+sKu5mAQUK+/sHxP1KY+XEbac3cHQPaGpX1wDdIWMZldiRsKulHpUKTUaaj4DLJv5kmqL\n4YcVd/UROTrlDGVosmk+PsnyHwzssIfMdLG6C1U3aJ2JQQa9l7WNbRLme0wS/+0n+1rlDVXz8UnE\nS/ngaI+Nb888kQ+k3QdxA+QFlTVIPhlg48ld2MnqJxt6Z5Y1j/ZitlUuWrx21QHVoygbNv97O72X\ntDkXNTW6h+EMzjaaiyy9erBiOpLVWZroJO4XQZUxGLi2mWKiRv9QU6DFXbOrMJtVMacBv5jF49UM\nq8Nm8TeG2OO3W9n9N1vpujCGEaydN4l/7zyeZYVJKk6ctvzoLWHe+GgXb3yom56vtLHxk11sPLWT\n4sh2IbPabZbf1udUtYhCPIqmD6ZZdt0A/n1zjidL2cSjCbXqSigmhfgvJq9JN0xndJ8E7LG7DQnY\neJYWaf3k5OZmvZe1kH7WPyGlImA5pZG7PdZTNVJffMUgRsSuai0sHsj+be4NwkbR4q7ZFZgyxy4i\njwPdLk9dopR6uPSaS3Cqn384yXHOAM4A6OheulOL3VURgWU3DND7lVZSf/Dj6tmSFQZvah4rCRw1\n8cq85GXbN1pZ8p3o2Et9uxVYcUu/M8rOKHerXHLlIPG1QWIPhci87HGvxMkYznNTEDwgy6qfbCP2\nYJB8j0XooCzhI1NlE6MmUug3GPlFyP0cC0J+g2fSYd2+3QqseaSXTWd0kH3JW3EcVQSjipmaRqNx\nmFLYlVJHTPa8iJwCHAMcrpSqGpIqpW4EbgRYs9e+9bHuqyNWq82y6weJ3hti8JrmCT4upa/Drc47\nLyT+O4CdoaLcz23sm1jQ/OEU4SPSvPbeJbgbfzklhNPB012k43PTr0ZJ/8Xr3ulb+lxryeSbxOB0\n4Xb+3xhbPt9Rnp83FNaiYoWHz1yjN1M1852ZVsUcDXwJeI9SavLE6wIlv9Vk+IEQ+c0WgQOzNB+b\nIr/eIv5QGPEo7CKlKpZJ8saqNNBjXKdo8vc++q9uJrfeg9VZpP3MeJlXjZg4iTa34Fag6Zja/HMN\n3ROuOu0OE1r/1T2No5QzajC33sK3e57AO3J0nBNj4OpmxONE6lZ3kWXX1m4vRKNpFGZax34d4AMe\nE+d/2zNKqc/OeFUNQupPPrZ8oX3MJTH5Wz9Dd0RYeXcfbaeNkH3ZixGx2fzZzqpt/ACepQXMpnGi\n/qyPree1j0X9hR6LvitaUGmh5eNOGaIRUAQPyDo17+NLF0XRdEKiqt3wzqIUxB4Okvmzj2p3Ca1n\nxFxN1YojpUHhG7b/Ovr2zLPs+gGaj0mRecmL2Wzj3SM/b0RdR+2a+cxMq2J2V0otV0q9vfSjRb2E\nUtB7aavTcTlqZ5sxKPSbDN4awdNlE35PhuB+Ofz75Nw3C8WpIum+dKjs4YFrJ6ZynGMP3NBU1n7f\nfVkUz2Kn1V98NhKwCeyfpeu8yYeD7My59lzcRt+3WpjszqPlQ+53CX1XtJB9zYNKG2M/2Zc89H+v\nCSOkCB6Yxfem+SPqGs18Z0F4xdSDQo/pWO1OJC8kfh0oe2jx5VHM9qLjtWIp8CiMsE3TCQlW3ruN\nwDvKm3LGu0iOx04aZWWMVqfNqge3seTKQTrPi7HshgGW/WBg0s3PiSgFxZigqqS1s//wsPlzHSQe\nDUxiEawcw7Jk5fPKhpHHghWbvCpnMPLz+tSsTxddIaOZryw4S4G5QvyVM0lHGfUnH8WzpMiatb0k\nnvJT6LHwvTlPYP9s1QjVs7RA7tXKkj8joCrKNsWE0CFZYPpjAEeJPx6g/zstFGMGYjgeM13nxsYa\nuFLPe9ly9ugG52ThtIBSbL2wnVX3byt7RtlUTUO5DQqfb+iUjGY+oiP2GmG12fj2zlW4MorPRoni\n1UOWsO59i+m/tgmVL1kGHJ6h9eQEwQOqizo4booVNsQeReun4q6VMjtD6k8+tl3aSnHAHGtuij8U\nou+KlrHXbPtWKdU0qaiPIuQ3m+QnWAzHHghV+S1UBA+tHBSu0WimRgt7DVl8xSCepaUcd7DkmVIU\n8q97UFkDO2YyfE+YrRfumCd7+J8ytJ486rNeunAoRexnobJmppkweFPE1Ts9/nPnM+ws5DfsxA3f\nhOtR9KYm9zsbA7rOn9e2Q2PolIxmvqGFvYZ4upwc99LvDbDoK0M0n5BADFXWkamyBqlnfGUVIVOh\nbIg9HGbMxRGgYFDsNYneGZmVtec3V1mPpShGTcQD4up/Ux2r08Zasr3IXRVx34cAMJwU1a6CFnfN\nfEILe40RcQzDmo5Ok9tkoXKVX7lYuPrCVCO/ycJ28UtROYPEYwGXd+w4/r2rVOoosBYVEKPkW+Ob\nugtU/DZGyGbxFYNlKSYxwariQ+9dPnUjk0ajcUcL+xzi2yPv6vJo5x1r3+zr00uQi1+5DvuAyo3Z\nnaX9zHhpFN44F0y/Tdvp8bEO2I5zYoTfVzIeczPu8tgEDkzTeU6M1Wt78O9VWVrTcU6sYr9AfDYd\nX4yR32Ky7fIW1p+4iK0XtJF5aRq2m3VER+2a+YKuiplDWj6WZPjH4VLp4KgwK8gJg1e3MHg1mF1F\nVv5oG1ZrdYH2LCri3T1P9hVPWX5a/DbNJ05u0DVdfLsVWH5rPwPXNJH5mw+zrUjb6SM0/fP2WnTD\nC4u/NURhIEbiKT99/68FUY7FrgQV/jfnWXbd4KQ2yE1HpzF8ioHrmslvNfGsKND5hTieJQXWf2KR\nU3FTFHKvWyR/52fxd6LOQA+NRlMVmcTepWas2Wtf9c0fPjLnnzsfyLziYds3WxyDK6G0mVg+0s5a\nXGDNz7e5H6BEfqvJpjM6KQ6XbrqKED4yTffXhib1hq8lxZgw8qsghQGTwDuyBA/O7vRatnyxneTT\nEx0iwVpcYPXa3nndrKTLHzW14kM/euV5pdQBU71OR+xzjP/NeVbe1Y/Kw6vvWgL2ROUTCj0W+T4D\nT5fLQI08FIYMrM4iq/+rl/SffBT6TfxvzeJdUd/NRrNZ0fKx6U1Wmor0n30Vog5QGDCxYwbmPHZ4\n1LXtmnqjhb1OiAd3N8cS+V6zTNiVguhtYaK3NjnuiQa0fmqE9jNG6h695ntMordESD3nw+oq0nbq\nSNm4vZ3BbC5ij7hsNAtOh+48R4u7pp7ozdM6YnYWcbVCFPDvUV4VMvzjENGbm1ApA5V1/FSG7ogw\ndFd4bhZbhXyPyYZPLCL2cIj8Jg/p5/1sPb+d4QdmZgfQekrCdVM18sEURv3mbGg0uwRa2OvIdnOv\n8eKuaD4+CTZlzUbRW5tcG4ait89O3frOEr0lgp2SsiodlTHov6YZewZzp5uPT9Ly8QTic3xzxKsI\nvTtD15eGpn7zPEFXyWjqhU7F1JHQoVmW3djPtstbyG/1YIRsWk5MkH7Bx7r3LQHAt2eOxV8fohh1\nvwbbwwZKUbd0TOqPfvfSS+XU2/t227l6dBHoPCdO22kj5DdaWIuKWB3zPwWj0cwHtLDXmeABOVY/\n1Ac4G6OvH9vt+LOUyhizL3nZeFon3pUFcm9U1g16VhTqmmO3ugruXaoFcR2GvaOYEYW5d30nJmk0\nuxo6FTOPSDzlx04Y5d4pSlA5IXhouqLLU/w2nefPrrf6jtJ2qksu3GsTPCSD1aojbJ2O0dQDLezz\niPxWy9WqVqUNxANLrxsgsF8Gs6WI/+1Zll4zWPdmndBhGTrPiTkmZyEnFx58Z5bFl0enfvMCQYu7\nZq7RqZh5hH/PPOJRqAllkBK08e+VJ7h/juDNA3VaXXVaPp6k6SNJ8hstzDYbaxZSMI2GLn/UzCU6\nYp9HBA7M4tstj3jHCaPHxuoqEn5Pun4LmwaGF3y7F7SoT4KO3DVzhRb2eYQILPvBAC0nJTA7ipht\nRVpOSLLijr5J/VY0Go1mPDoVM88wAorOL8Tp/EK83kvR1ACdktHMBTpi12g0mgZDC7tmXqKUM3e1\n/5omBm+NVMxK3ZXRuXZNrdGpmFnETgu5NyzMjqKrM+NCRylQORDv5J2yyoaeL7WR/L0flRbwQPSm\nCN2XR4kcrr3YNZqp0BH7LDF4e5jX3r+YzWd2sv64bjZ/vp2iy/i6hYiyYeCGCK/90xLWHbaUN47p\nZuRJf9XXJ54MlETdAATygsoa9F7ahp1ujO9UR+2aWqKFfRYY+bWf6I1NqKyBnTRQOYPUn3z0frWt\n3kubFwxc28TQnRHspNNVW+ix6L2kjdQffa6vjz8SKIl6OWJA+gX39+yKaHHX1Aot7LPA0B2RCudF\ncgapP/i3TzhaoNgZnHGALs6UW89vY927l/DGRxYRWxtkdJiXTJYgNOd+4lct0eKuqQULW3VmicJg\nlY09U1GMLeyvuDhUfdPTTpjYSYP8Bg9932ph6E7HW775uCQScNmjEAjuP7MBHhrNQmBhq84sETw4\n4xpJigc8S3fOtrZRsDqKVX7Lyr8vlTEYvKkJOwfBQ7M0fyiJ+GzEayMB52fJVZMPxt5V0VG7ZrbR\nVTGzQPtnRkg8EcBOGaVxdwrxKzovGJo8rbAAEA+0nR4netPEQSHuHu6FPhPvsiJdF8ZoOTFJ8hk/\nRtgm/L40Zrix0jAaTa1Y4LIzO3gWF1l53zaGbo+Qes6PtaRA2ykjBPebwQiheYzKO5Ur6b958K4o\nEvlAalLRbft0ArPZJnpLE8WoCaZCpVzCeFvKvGa8qwt4VydqcQrzDt2RqplNtLDPEp4um64LY0B9\n/dFrTTEubDyli0K/iUoZSMBm4NomVtzej3eVe9pJBFqOT9FyfAqA1LM+tpzbXhbBi9+m6bgkRnDh\nRuVa3DWzhc6xa3aIgeubHd/4UsSt0gb2iEHvpa3TPkbw4CyLLhtyhnlbCvHbNH80SVedh4ZoNI2C\njtg1O0TisQDkJ+THlZB5xUsxIdPOgzcdmSZyRBo7IRh+1ZCbojuDjto1s4GO2DU7xiS/MbKDv00i\nzkxTLerl6CoZzUzRwq7ZIZqOSZUPAgEwFYG3Zxd0flyjmU9oYdfsEO1nxvG9Ke80EHkUErSxLYDG\nzwAABMlJREFUOop0f32o3ktrKHTUrpkJs5JjF5HzgSuBTqXU/BvKqZk1jIBi+R39pJ/3kX3Fg2dp\ngdC7MjqdUgN0vl2zs8xY2EVkOXAksHHmy9HsCohA8IAswQN0e79GMx+ZjVTMd4ELmdgjrtFoNJq6\nMCNhF5HjgC1KqRdnaT0ajWYcOteu2RmmTMWIyONAt8tTlwAXA0dN54NE5AzgDICO7qU7sESNZmGj\nc+2aHWXKiF0pdYRSap+JP8DrwGrgRRFZDywDXhARt4sASqkblVIHKKUOiLTqARQazY6gI3fNjrDT\nqRil1F+VUl1KqVVKqVXAZmA/pVTvrK1Oo9GMocVdM110HbtGo9E0GLMm7KXIXdewazQ1REftmumg\nI3aNRqNpMLSwazQaTYOhhV2j2cXQ6RjNVGhh12h2QbS4ayZDC7tGs4uixV1TDS3sGo1G02BoYddo\ndmF01K5xQ5Sae1NGEekHNszRx3UAC6m+fiGd70I6V9Dn2+hM53xXKqU6pzpQXYR9LhGRPymlDqj3\nOuaKhXS+C+lcQZ9vozOb56tTMRqNRtNgaGHXaDSaBmMhCPuN9V7AHLOQznchnSvo8210Zu18Gz7H\nrtFoNAuNhRCxazQazYJiQQm7iJwvIkpEOuq9llohIleKyCsi8hcReVBEWuq9plogIkeLyN9FZJ2I\nfLne66klIrJcRJ4UkZdF5G8ick6911RrRMQUkT+LyNp6r6XWiEiLiDxQ+n/7sogcMtNjLhhhF5Hl\nwJHAxnqvpcY8BuyjlNoX+AdwUZ3XM+uIiAlcD3wQ2Av4FxHZq76rqikF4Dyl1FuAdwJnNfj5ApwD\nvFzvRcwR1wC/VEq9GXgbs3DeC0bYge8CFwINvamglHpUKVUo/fUZnFm0jcZBwDql1OtKqRxwL/Ch\nOq+pZiilepRSL5T+PILzH79hJ8KLyDLgn4Gb672WWiMiTcA/AbcAKKVySqnhmR53QQi7iBwHbFFK\nvVjvtcwxpwG/qPciasBSYNO4v2+mgYVuPCKyCngH8Gx9V1JTrsYJwux6L2QOWAP0A7eVUk83i0ho\npge1Zr6u+YGIPA50uzx1CXAxcNTcrqh2THauSqmHS6+5BOcW/odzubY5Qlwea+g7MQARCQM/Ab6o\nlIrXez21QESOAfqUUs+LyHvrvZ45wAL2A85WSj0rItcAXwa+OtODNgRKqSPcHheRtwKrgRdFBJzU\nxAsicpBSqncOlzhrVDvXUUTkFOAY4HDVmPWsm4Hl4/6+DNhap7XMCSLiwRH1Hyqlflrv9dSQw4Dj\nROT/AH6gSUTuVkqdXOd11YrNwGal1Ogd2AM4wj4jFlwdu4isBw5o1MHbInI0cBXwHqVUf73XUwtE\nxMLZGD4c2AI8B5yklPpbXRdWI8SJSO4AokqpL9Z7PXNFKWI/Xyl1TL3XUktE5Gng35RSfxeRrwEh\npdQFMzlmw0TsmjGuA3zAY6U7lGeUUp+t75JmF6VUQUQ+D/wKMIFbG1XUSxwGfBL4q4j8T+mxi5VS\nj9RxTZrZ42zghyLiBV4HTp3pARdcxK7RaDSNzoKoitFoNJqFhBZ2jUajaTC0sGs0Gk2DoYVdo9Fo\nGgwt7BqNRtNgaGHXaDSaBkMLu0aj0TQYWtg1Go2mwfj/nLs74KL9m+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19e85dac6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from Util import visualize2d\n",
    "\n",
    "visualize2d(perceptron, x, y)\n",
    "visualize2d(perceptron, x, y, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 可视化训练过程\n",
    "\n",
    "+ 实现思路如下：\n",
    "    + 在每一步迭代时生成一张如上所示的图像\n",
    "    + 在最后调用相应的第三方库（`imageio`）、将生成的所有图像合成一个 mp4\n",
    "    + 用`ffmpeg`将 mp4 转为方便分享的 gif\n",
    "\n",
    "![perceptron](https://cdn.rawgit.com/carefree0910/Resources/cbd5675e/Lines/Perceptron.gif)\n",
    "\n",
    "![perceptron](https://cdn.rawgit.com/carefree0910/Resources/cbd5675e/Backgrounds/Perceptron.gif)"
   ]
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